<?xml version='1.0' encoding='utf-8'?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.2 20190208//EN" "http://jats.nlm.nih.gov/publishing/1.2/JATS-journalpublishing1.dtd">
<article article-type="research-article" dtd-version="1.2" xml:lang="ru" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><front><journal-meta><journal-id journal-id-type="issn">2518-1092</journal-id><journal-title-group><journal-title>Research result. Information technologies</journal-title></journal-title-group><issn pub-type="epub">2518-1092</issn></journal-meta><article-meta><article-id pub-id-type="doi">10.18413/2518-1092-2026-11-2-0-5</article-id><article-id pub-id-type="publisher-id">4255</article-id><article-categories><subj-group subj-group-type="heading"><subject>INFORMATION SYSTEM AND TECHNOLOGIES</subject></subj-group></article-categories><title-group><article-title>&lt;strong&gt;ADAPTIVE MULTI-INTERVAL SCALE (AMIS):&amp;nbsp;A NORMALIZATION ALGORITHM FOR AGGREGATED DATA IN A UNIFIED METRIC SPACE&lt;/strong&gt;</article-title><trans-title-group xml:lang="en"><trans-title>&lt;strong&gt;ADAPTIVE MULTI-INTERVAL SCALE (AMIS):&amp;nbsp;A NORMALIZATION ALGORITHM FOR AGGREGATED DATA IN A UNIFIED METRIC SPACE&lt;/strong&gt;</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="ru"><surname>Kravtsov</surname><given-names>Gennady Grigorievich</given-names></name><name xml:lang="en"><surname>Kravtsov</surname><given-names>Gennady Grigorievich</given-names></name></name-alternatives><email>62abc@mail.ru</email></contrib></contrib-group><pub-date pub-type="epub"><year>2026</year></pub-date><volume>11</volume><issue>2</issue><fpage>0</fpage><lpage>0</lpage><abstract xml:lang="ru"><p>The article addresses the problem of methodological incorrectness in the comparative analysis of heterogeneous data, including data presented in aggregated form. Existing normalization methods are either inapplicable to aggregated data or fail to ensure interpretability and metric rigor.
A method is proposed&amp;ndash;an extension of the author&amp;#39;s adaptive multi-interval scale (AMIS)&amp;ndash;as a software and methodological framework for normalizing and comparing aggregated data. Algorithms have been developed for converting aggregated data into representative samples (exact and optimized), along with an inverse transformation mechanism that establishes quantitative correspondences between original scales through the universal AMIS metric. The method was tested on three tasks: normalization and comparison of current academic grades, aggregated Unified State Exam results, and macroeconomic GDP indicators. The results demonstrate that AMIS creates a unified metric space for various data types, ensuring the correctness of arithmetic operations and statistically grounded correspondences between the original scales. The proposed approach solves the fundamental problem of integrating heterogeneous aggregated data. The open software suite (Python, C#, Excel) and verified data in repositories ensure full reproducibility of the results.</p></abstract><trans-abstract xml:lang="en"><p>The article addresses the problem of methodological incorrectness in the comparative analysis of heterogeneous data, including data presented in aggregated form. Existing normalization methods are either inapplicable to aggregated data or fail to ensure interpretability and metric rigor.
A method is proposed&amp;ndash;an extension of the author&amp;#39;s adaptive multi-interval scale (AMIS)&amp;ndash;as a software and methodological framework for normalizing and comparing aggregated data. Algorithms have been developed for converting aggregated data into representative samples (exact and optimized), along with an inverse transformation mechanism that establishes quantitative correspondences between original scales through the universal AMIS metric. The method was tested on three tasks: normalization and comparison of current academic grades, aggregated Unified State Exam results, and macroeconomic GDP indicators. The results demonstrate that AMIS creates a unified metric space for various data types, ensuring the correctness of arithmetic operations and statistically grounded correspondences between the original scales. The proposed approach solves the fundamental problem of integrating heterogeneous aggregated data. The open software suite (Python, C#, Excel) and verified data in repositories ensure full reproducibility of the results.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>adaptive multi-interval scale (AMIS)</kwd><kwd>data normalization</kwd><kwd>aggregated data</kwd><kwd>inverse transformation</kwd><kwd>unified metric space</kwd><kwd>comparison of heterogeneous metrics</kwd><kwd>interdisciplinary research</kwd><kwd>educational analytics</kwd><kwd>economic indicators</kwd></kwd-group><kwd-group xml:lang="en"><kwd>adaptive multi-interval scale (AMIS)</kwd><kwd>data normalization</kwd><kwd>aggregated data</kwd><kwd>inverse transformation</kwd><kwd>unified metric space</kwd><kwd>comparison of heterogeneous metrics</kwd><kwd>interdisciplinary research</kwd><kwd>educational analytics</kwd><kwd>economic indicators</kwd></kwd-group></article-meta></front><back><ref-list><title>Список литературы</title><ref id="B1"><mixed-citation>Avanesov V.S. Scaling of Test Results.&amp;nbsp;Pedagogical Measurements. 2013. No. 2. P. 3&amp;ndash;21. (In Russian)</mixed-citation></ref><ref id="B2"><mixed-citation>Gordeeva T.O., Sychev O.A., Sidneva A.N. Assessment of Schoolchildren&amp;#39;s Achievements in Traditional and Developmental Education Systems: A Psychological and Pedagogical Analysis.&amp;nbsp;Educational Studies. 2021. No.&amp;nbsp;1. P. 213&amp;ndash;236. DOI: 10.17323/1814-9545-2021-1-213-236. (In Russian)</mixed-citation></ref><ref id="B3"><mixed-citation>Dvoeryadkina N.N., Chalkina N.A. Data Standardization in the Organization of Psychological and Pedagogical Research.&amp;nbsp;Bulletin of AmSU. 2016. No. 74. (In Russian)</mixed-citation></ref><ref id="B4"><mixed-citation>Koklev P.S. Company Valuation Using Machine Learning Methods.&amp;nbsp;Finance: Theory and Practice. 2022. Vol. 26, No. 5. P. 132&amp;ndash;148. DOI: 10.26794/2587-5671-2022-26-5-132-148. (In Russian)</mixed-citation></ref><ref id="B5"><mixed-citation>Kravtsov G.G.&amp;nbsp;Introduction to the Analytical Method of Education Control (AMEC): From Mathematical Analytics of the Educational Process to a Standardized Educational Database. Ryazan: Research Center &amp;quot;Applied Statistics&amp;quot;, 2025. DOI: 10.5281/zenodo.16791743. (In Russian)</mixed-citation></ref><ref id="B6"><mixed-citation>Orlov A.I. Measurement Theory as a Part of Data Analysis Methods.&amp;nbsp;Sociology: Methodology, Methods, Mathematical Modeling. 2012. No. 35. P. 155&amp;ndash;174. (In Russian)</mixed-citation></ref><ref id="B7"><mixed-citation>Potanina A.M., Morosanova V.I. Differential Aspects of Regulatory and Personal Resources of Students&amp;#39; Academic Performance with Different Profiles of School Engagement.&amp;nbsp;Theoretical and Experimental Psychology. 2023. Vol. 16, No. 4. P. 218&amp;ndash;239. DOI: 10.11621/TEP-23-37. (In Russian)</mixed-citation></ref><ref id="B8"><mixed-citation>Sorokin A.A. Application of Piecewise Functions for Normalization of Input Variables in Fuzzy Inference Systems.&amp;nbsp;Information Technologies in Management. 2021. No. 4. P. 70&amp;ndash;76. DOI: 10.25728/pu.2021.4.6. (In Russian)</mixed-citation></ref><ref id="B9"><mixed-citation>Starovoitov V.V., Golub I.A. Data Normalization in Machine Learning.&amp;nbsp;System Analysis and Applied Informatics. 2021. No. 3. P. 52&amp;ndash;60. (In Russian)</mixed-citation></ref><ref id="B10"><mixed-citation>Arachchige C.N.P., Prendergast L.A., Staudte R.G. Robust analogs to the coefficient of variation.&amp;nbsp;Journal of Applied Statistics. 2024. Vol. 51, No. 3. P. 576&amp;ndash;598. DOI: 10.1080/02664763.2022.2137452.</mixed-citation></ref><ref id="B11"><mixed-citation>Bonofiglio F., Schumacher M., Binder H. Recovery of original individual person data (IPD) inferences from empirical IPD summaries only: Applications to distributed computing under disclosure constraints.&amp;nbsp;Statistics in Medicine. 2020. Vol. 39, No. 8. P. 1183&amp;ndash;1198. DOI: 10.1002/sim.8470.</mixed-citation></ref><ref id="B12"><mixed-citation>Bruffaerts C., Verardi V., Vermandele C. A generalized boxplot for skewed and heavy-tailed distributions.&amp;nbsp;Statistics &amp;amp; Probability Letters. 2014. Vol. 95. P. 110&amp;ndash;117. DOI: 10.1016/j.spl.2014.08.016.</mixed-citation></ref><ref id="B13"><mixed-citation>B&amp;uuml;rkner P.C., Vuorre M. Ordinal Regression Models in Psychology: A Tutorial.&amp;nbsp;Advances in Methods and Practices in Psychological Science. 2023. Vol. 6, No. 1. DOI: 10.1177/25152459231113332.</mixed-citation></ref><ref id="B14"><mixed-citation>De Ayala R.J.&amp;nbsp;The Theory and Practice of Item Response Theory. 2nd ed. New York: Guilford Press, 2022. 658 p.</mixed-citation></ref><ref id="B15"><mixed-citation>Heitjan D.F., Rubin D.B. Inference from Coarse Data via Multiple Imputation with Application to Age Heaping.&amp;nbsp;Journal of the American Statistical Association. 1990. Vol. 85, No. 410. P. 304&amp;ndash;314. DOI: 10.1080/01621459.1990.10476205.</mixed-citation></ref><ref id="B16"><mixed-citation>Hubert M., Vandervieren E. An adjusted boxplot for skewed distributions.&amp;nbsp;Computational Statistics &amp;amp; Data Analysis. 2008. Vol. 52, No. 12. P. 5186&amp;ndash;5201. DOI: 10.1016/j.csda.2007.11.008.</mixed-citation></ref><ref id="B17"><mixed-citation>Jain A., Nandakumar K., Ross A. Score normalization in multimodal biometric systems.&amp;nbsp;Pattern Recognition. 2005. Vol. 38, No. 12. P. 2270&amp;ndash;2285. DOI: 10.1016/j.patcog.2005.01.012.</mixed-citation></ref><ref id="B18"><mixed-citation>Kravtsov G.&amp;nbsp;Universal Adaptive Normalization Scale (AMIS): A Methodology for Integrating Heterogeneous Social and Educational Metrics&amp;nbsp;[Preprint]. OSF. 2025. DOI: 10.17605/OSF.IO/BDT2K.</mixed-citation></ref><ref id="B19"><mixed-citation>Kravtsov G. AMIS_Normalization_Tool [Software].&amp;nbsp;GitHub. 2026. URL:&amp;nbsp;https://github.com/Famimot/AMIS_Normalization_Tool&amp;nbsp;(accessed: 13.02.2026).</mixed-citation></ref><ref id="B20"><mixed-citation>Kravtsov G. AMIS_Excel_Plugin [Software].&amp;nbsp;GitHub. 2026. URL:&amp;nbsp;https://github.com/Famimot/AMIS_Excel_Plugin&amp;nbsp;(accessed: 13.02.2026).</mixed-citation></ref><ref id="B21"><mixed-citation>Kravtsov G. Adaptive Multi-Interval Scale (AMIS): Open-Source Software, Source Data and Results for Normalizing and Comparing Raw &amp;amp; Aggregated Metrics [Data set].&amp;nbsp;Harvard Dataverse. 2025. V1. URL:&amp;nbsp;https://doi.org/10.7910/DVN/HXSED6&amp;nbsp;(accessed: 13.02.2026).</mixed-citation></ref><ref id="B22"><mixed-citation>Lu Y., Wang L., Lu J., Yang J., Shen C. A robust data scaling algorithm to improve classification accuracies in biomedical data.&amp;nbsp;BMC Bioinformatics. 2016. Vol. 17, Suppl. 13. P. 359. DOI: 10.1186/s12859-016-1236-x.</mixed-citation></ref><ref id="B23"><mixed-citation>Stevens S.S. On the theory of scales of measurement.&amp;nbsp;Science. 1946. Vol. 103, No. 2684. P. 677&amp;ndash;680. DOI: 10.1126/science.103.2684.677.</mixed-citation></ref><ref id="B24"><mixed-citation>Tao Y., Meng Y., Gao Z., Yang X. Perceived teacher support, student engagement, and academic achievement: A meta-analysis.&amp;nbsp;Educational Psychology. 2022. Vol. 42, No. 4. P. 401&amp;ndash;420. DOI: 10.1080/01443410.2022.2033168.</mixed-citation></ref><ref id="B25"><mixed-citation>van der Linden W.J., ed.&amp;nbsp;Handbook of Item Response Theory, Volume Three: Applications. 1st ed. Boca Raton: Chapman and Hall/CRC, 2022. DOI: 10.1201/9781315117430.</mixed-citation></ref></ref-list></back></article>